Third order nodal finite element methods with transverse and reduced integration for elliptic problems

Applied Numerical Mathematics

Volumn 46, Issue 2, 2003, Pages 209-230

  Hennart, J P ^a   Mund, E H ^b,c   Del Valle, E ^d  

^a UNIVERSIDAD NACIONAL AUTÓNOMA DE MÉXICO   (Mexico)

^b UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

^c UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

^d INSTITUTO POLITÉCNICO NACIONAL   (Mexico)

Author keywords

Diffusion processes; High order schemes; Nodal methods; Variational methods

Indexed keywords

COMPUTATIONAL METHODS; DIFFUSION; FINITE ELEMENT METHOD; HEURISTIC METHODS; INTEGRATION; VARIATIONAL TECHNIQUES;

ELLIPTIC PROBLEMS;

PROBLEM SOLVING;

EID: 0038790030     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-9274(03)00024-2     Document Type: Article

References (22)

1. Brezzi F., Douglas J., Marini L.D. Two families of mixed finite elements for second order elliptic problems. Numer. Math. 47:1985;217-235.
2. Brezzi F., Douglas J., Fortin M., Marini L.D. Efficient rectangular mixed finite elements in two and three space variables. Math. Models Numer. Anal. 21:1985;581.
3. Brezzi F., Fortin M. Mixed and Hybrid Finite Element Methods. 1991;Springer, Berlin.
4. Carey G.F., Oden J.T. Finite Elements: A Second Course. 1983;Prentice-Hall, Englewood Cliffs, NJ.
5. Dorning J.J. Modern coarse-mesh methods - A development of the 70s. Proceedings Int. Conf. Comput. Methods Nucl. Engng., Vol. 1. 1979;ANS M&C, Williamsburg, VI. 3.1-3.31.
6. C. Fedon-Magnaud, Etude Théorique de Quelques Méthodes Nodales de Résolution de l'Équation de Diffusion - Tests Numériques, Thesis, Univ. Paris VI, 1983.
7. Fedon-Magnaud C., Hennart J.P., Lautard J.J. On the relationship between some nodal schemes and the finite element method in static diffusion calculations. Proc. Int. Topl. Mtg. on Advances in Reactor Computations, Salt Lake City, NV, March 28-31, 1983. 1983;American Nuclear Society.
8. Gladwell I., Wait R. A Survey of Numerical Methods for Partial Differential Equations. 1979;Clarendon, Oxford.
9. Hennart J.P., Mund E.H. Singularities in the finite element approximation of two-dimensional diffusion problems. Nuclear Sci. Engrg. 62:1977;55-68.
10. Hennart J.P. A general family of nodal schemes. SIAM J. Sci. Statist. Comput. 3:1986;264-287.
11. Hennart J.P. On the numerical analysis of analytical nodal methods. Numer. Methods Partial Differential Equations. 4:1988;233.
12. Hennart J.P., Jaffré J., Roberts J.E. A constructive method for deriving finite elements of nodal type. Numer. Math. 53:1988;701-738.
13. Hennart J.P., Malambu E.M., Mund E.H., del Valle E. Efficient higher order nodal finite element formulations for neutron multigroup diffusion equations. Nuclear Sci. Engrg. 124:1996;97-110.
14. Hennart J.P., Mund E.H., del Valle E. A composite nodal finite element method for hexagons. Nuclear Sci. Engrg. 127:1997;139-153.
15. Hennart J.P., del Valle E. Mesh-centered finite differences from nodal finite elements for elliptic problems. Numer. Methods Partial Differential Equations. 14:1998;439-465.
16. Lawrence R.D. Progress in nodal methods for the solution of the neutron diffusion and transport equations. Progr. Nucl. Energy. 17:1986;271.
17. Mosé R., Siegel P., Ackerer P., Chavent G. Application of the mixed hybrid finite element approximation in a groundwater flow model: Luxury or necessity? Water Resources Res. 30:1994;3001-3012.
18. Moulton J.D., Morel J.E., Ascher U.M. Approximate Schur complement preconditioning of the lowest-order nodal discretizations. SIAM J. Sci. Comput. 19:1998;185-205.
19. Saad Y. Iterative Methods for Sparse Linear Systems. 1995;PSW, Boston, MA.
20. Schwab Ch. p-and hp-Finite Element Methods. Theory and Applications in Solid and Fluid Mechanics. 1998;Clarendon Press, Oxford.
21. Strang G., Fix G.J. An Analysis of the Finite Element Method. 1973;Prentice-Hall, Englewood Cliffs, NJ.
22. Wagner M.R., Koebke K. Progress in nodal reactor analysis. Atomkernenergie. 43:1983;119-131.